计算机与现代化 ›› 2011, Vol. 193 ›› Issue (9): 156-158,.doi: 0.3969/j.issn.1006-2475.2011.09.042
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郗艳华
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XI Yan-hua
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摘要： 分析三角形式傅里叶级数中周期信号的分解与合成,用 Matlab软件对方波信号的分解与合成进行仿真。结果显示方波信号可以分解成直流分量和不同频率余弦分量（或正弦分量）的叠加；满足一定关系的直流信号和有限次谐波分量之和可以近似表示方波信号,对方波信号合成过程中误差和吉布斯现象进行分析。利用 Matlab软件仿真可以直观地理解周期信号的分解与合成原理，它对于建立信号频谱的概念以及系统频谱分析都有非常重要作用。
关键词: 周期信号, 分解与合成, 吉布斯现象
Abstract: Decomposition and composition of periodic signal is analyzed with trigonometric form of Fourier series in signal and linear systems， and square wave’s decomposition and composition is simulated with Matlab. The experiment result shows that the square wave can be decomposed into the summation of DC component and different frequency cosine components (or sine components). The sum of the DC signal and limited harmonic components under certain conditions can be approximated the square wave. The error and Gibbs phenomenon are analyzed in the process of square wave’s composition. The principle of periodic signal’s decomposition and composition can be comprehended with software simulation, it is very important to understand the concept of the signal spectrum and the system’s spectrum analysis.
Key words: periodic signal, signal’s decomposition and composition, Gibbs phenomenon
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TN702
郗艳华. 基于Matlab周期信号的分解与合成[J]. 计算机与现代化, 2011, 193(9): 156-158,.
XI Yan-hua. Periodic Signal’s Decomposition and Composition Based on Matlab[J]. Computer and Modernization, 2011, 193(9): 156-158,.
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链接本文: http://www.c-a-m.org.cn/CN/0.3969/j.issn.1006-2475.2011.09.042
http://www.c-a-m.org.cn/CN/Y2011/V193/I9/156
